Information on Result #547825
There is no linear OA(418, 32, F4, 14) (dual of [32, 14, 15]-code), because construction Y1 would yield
- linear OA(417, 21, F4, 14) (dual of [21, 4, 15]-code), but
- 2 times truncation [i] would yield linear OA(415, 19, F4, 12) (dual of [19, 4, 13]-code), but
- construction Y1 [i] would yield
- OA(414, 16, S4, 12), but
- the (dual) Plotkin bound shows that M ≥ 4294 967296 / 13 > 414 [i]
- linear OA(44, 19, F4, 3) (dual of [19, 15, 4]-code or 19-cap in PG(3,4)), but
- discarding factors / shortening the dual code would yield linear OA(44, 18, F4, 3) (dual of [18, 14, 4]-code or 18-cap in PG(3,4)), but
- OA(414, 16, S4, 12), but
- construction Y1 [i] would yield
- 2 times truncation [i] would yield linear OA(415, 19, F4, 12) (dual of [19, 4, 13]-code), but
- OA(414, 32, S4, 11), but
- the linear programming bound shows that M ≥ 1976 281134 530560 / 7 232221 > 414 [i]
Mode: Bound (linear).
Optimality
Show details for fixed k and m, n and k, k and s, k and t, n and m, m and s, m and t, n and s, n and t.
Compare with Markus Grassl’s online database of code parameters.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | No linear OA(414, 32, F4, 10) (dual of [32, 18, 11]-code) | [i] | Construction Y1 (Bound) | |